Lecture Notes

1. Chapter 1:Introduction
   • Natural,Rational and Real Number Sets
   • §4:The Completeness Axiom
2. Chapter 2:Sequences
   • §7:Limits of Sequences
   • §9:Limit Theorems for Sequences
   • §10:Monotone Sequences and Cauchy Sequences
   • §11:Subsequences
3. Chapter 3:Continuity
4. Chapter 4:Sequences and Series of Functions
5. Chapter 5:Differentiation
6. Chapter 6:Integration
7. Proofs
   1. Ch.1
   2. Ch.2
   3. Ch.3
   4. Ch.4
   5. Ch.5
   6. Ch.6

-Natural Number Set ℕ: the set of all positive integers {1,2,3,4,…}

• If 1 is in ℕ, then so is n+1

-Set of all Integers ℤ: {0,-1,1,-2,2,…} -Rational Number Set ℚ: numbers of the form m/n, m and n ∈ ℤ -Real Number Set: